Estimation of Stopping Times for Stopped Self-Similar Random Processes

2019/05/24 by Schulmann, Viktor
#60G18 #60G40 #62G07 #62G20 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1905.10165

Abstract

Let X=(X_t)_{t≥ 0} be a known process and T an unknown random time independent of X. Our goal is to derive the distribution of T based on an iid sample of X_T. Belomestny and Schoenmakers (2015) propose a solution based the Mellin transform in case where X is a Brownian motion. Applying their technique we construct a non-parametric estimator for the density of T for a self-similar one-dimensional process X. We calculate the minimax convergence rate of our estimator in some examples with a particular focus on Bessel processes where we also show asymptotic normality.

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